A coupled immersed boundary‐lattice Boltzmann method with smoothed point interpolation method for fluid‐structure interaction problems

The immersed boundary‐lattice Boltzmann method has been verified to be an effective tool for fluid‐structure interaction simulation associated with thin and flexible bodies. The newly developed smoothed point interpolation method (S‐PIM) can handle the largely deformable solids owing to its softened model stiffness and insensitivity to mesh distortion. In this work, a novel coupled method has been proposed by combining the immersed boundary‐lattice Boltzmann method with the S‐PIM for fluid‐structure interaction problems with large‐displacement solids. The proposed method preserves the simplicity of the lattice Boltzmann method for fluid solvers, utilizes the S‐PIM to establish the realistic constitutive laws for nonlinear solids, and avoids mesh regeneration based on the frame of the immersed boundary method. Both two‐ and three‐dimensional numerical examples have been carried out to validate the accuracy, convergence, and stability of the proposed method in consideration of comparative results with referenced solutions.     

Shape morphing and topology optimization of fluid channels by explicit boundary tracking

An integrated shape morphing and topology optimization approach based on the deformable simplicial complex methodology is developed to address Stokes and Navier‐Stokes flow problems. The optimized geometry is interpreted by a set of piecewise linear curves embedded in a well‐formed triangular mesh, resulting in a physically well‐defined interface between fluid and impermeable regions. The shape evolution is realized by deforming the curves while maintaining a high‐quality mesh through adaption of the mesh near the structural boundary, rather than performing global remeshing. Topological changes are allowed through hole merging or splitting of islands. The finite element discretization used provides smooth and stable optimized boundaries for simple energy dissipation objectives. However, for more advanced problems, boundary oscillations are observed due to conflicts between the objective function and the minimum length scale imposed by the meshing algorithm. A surface regularization scheme is introduced to circumvent this issue, which is specifically tailored for the deformable simplicial complex approach. In contrast to other filter‐based regularization techniques, the scheme does not introduce additional control variables, and at the same time, it is based on a rigorous sensitivity analysis. Several numerical examples are presented to demonstrate the applicability of the approach.     

Stability of a rectangular plate under biaxial tension

The stability problem of a rectangular plate undergoing uniform biaxial in-plane tensile strain is solved using the three-dimensional equations of nonlinear elasticity. The surfaces of the plate are stress-free, and special boundary conditions that allow one to separate variables in the linearized equilibrium equations are specified on the lateral surfaces. For three particular models of incompressible materials, the critical curves are constructed and the instability region is determined in the plane of the loading parameters (the multiplicities of elongations of the plate material in the unperturbed equilibrium state). The numerical results show that for thin plates loaded by tensile stresses, the size and shape of the instability region depend only slightly on the relation among the length, width, and thickness of the plate. Based on the results obtained, a simple approximate stability criterion is proposed for an elastic plate under tensile loads. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 94–103, July–August, 2007.     

可变形多孔介质渗透系数的测定方法

在Ｂｉｏｔ理论基础上给出可变形多孔介质耦合渗流基本方程；求出小试件一维定常耦合渗流问题的解答；表明在一维流固耦合情况下试件内部压力梯度有明显的非均匀性。因此通过实验确定可变形多孔介质渗透系数在数学上可归结为微分方程的反问题，传统的测试渗透系数的方法需要改进。介绍了可变形多孔介质渗透系数的测试原理和测试方法。对粒状多孔材料实验的结果表明，传统实验方法得到的渗透系数误差较大。     

Phase Interaction in a Vapor-Liquid Medium in Transient Flow Regimes

A mathematical model and a numerical method are developed for studying nonlinear wave processes in two-phase liquids with gas or vapor bubbles under conditions of impact interaction with deformable media. On the basis of the proposed approach to the numerical modeling of the dynamics of the transient processes in the two-phase vapor-liquid and deformable media, the basic features of the phase behavior, the phase transitions, and the interphase heat and mass transfer, typical of liquids containing vapor bubbles, are analyzed. The results of solving problems of the dynamics of different vapor-liquid media are presented.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 88–102.Original Russian Text Copyright © 2005 by Petushkov.     

Local flows of a deformable damageable medium under impact interaction with a cavitating fluid

Local viscoplastic-flow and damage processes in a deformable medium induced by the collapse of dispersed vapor-gas bubbles in the near-wall layer of a cavitating fluid in the presence of propagating shock waves are investigated. The study is based on a generalized model developed for describing nonlinear deformations and flow of damageable media and on the results obtained earlier for local fluid flows induced by limiting transitions of vapor-gas bubbles.     

20单元双压电片变形镜对Zernike像差空间拟合能力的实验研究

利用20单元双压电片变形镜和13×13阵列哈特曼波前传感器所构成的闭环自适应光学系统,实验测试了双压电片变形镜对3～20项静态Zernike像差的空间校正能力,并将实验结果与仿真计算结果进行了对比.最后分析了哈特曼传感器与双压电片变形镜之间的对准误差对实验结果的影响.研究表明,除了少数几项外,双压电片变形镜对3～20项Zernike像差的拟合误差都小于0.5,各项Zernike仿真和实验结果之差平均小于0.1.计算表明,与严格对准的理想情况相比,双压电片变形镜对3～20项Zernike像差中大多数项的拟合误差都随着失配程度的增加而增大,对准精度对于高阶像差拟合效果的影响尤其严重.     

Study on the flow resistance of the dispersion system of deformable preformed particle gel in porous media using LBM-DEM-IMB method

After being injected into the porous media, the dispersion system of preformed particle gel (PPG) tends to enter high permeability regions and block water channeling passages, which forces the subsequent water to turn to the low permeability regions and thus increases sweep efficiency and enhances oil recovery. However, it is still unclear about the influence factors and the mechanisms how PPG increases water flow resistance, which limits the application of PPG in more oilfields. Therefore, the paper combines the lattice Boltzmann method (LBM), the discrete element method (DEM) and the improved immersed moving boundary (IMB) method to simulate the migration of deformable PPG in porous media. On the basis, the paper quantitatively analyzes the variation law of displacement pressure across the porous media and discusses the influence factors such as the PPG diameter, elasticity modulus and the number concentration. Results indicate that, because of the friction and retention of PPG in pore-throat, the displacement pressure across the porous media during PPG flooding is much higher than that during water flooding. In other words, the existence of PPG increases the flow resistance of injected water. Besides, the displacement pressure is always fluctuant resulting from the continuous process of PPG migration, retention, deformation and remigration. Influence factor analysis shows that the incremental value and fluctuation degree of flow resistance increase with the PPG diameter, elasticity modulus and the number concentration. The study not only provides useful reference for future PPG flooding, but also benefits the development of deformable particle flow theory.     

Inequality constraints with elastic impacts in deformable bodies. The convex case

Summary The aim of the present paper is to present some new results for problems when impacts occur. We prove, in the framework of linear elastic body, certain equivalent form of the d'Alembert's principle, including velocity discontinuity. We show that the theorem of stationary action still holds as an inequality. The consideration of the variation of the unknown impact time implies for the impact problem certain new variational expressions in inequality form. Received 13 August 1998; accepted for publication 6 May 1999